What is the average of even numbers from 37 to 173? Here we will show you how to calculate the average of even numbers from 37 to 173.
To find the average of the even numbers from 37 to 173, we first calculate how many even numbers there are from 37 to 173. Then, we calculate the sum of even numbers from 37 to 173. And finally, we divide the sum by the number of even numbers to get the average.
The range is from 37 to 173, and the even numbers within that range are from 38 to 172. Therefore, the first even number in the sequence is 38, and the last even number in the sequence is 172.
Step 1) Calculate the total number of even numbers from 37 to 173
Here we calculate the total number of even numbers from 37 to 173 by entering the first and last even number in the sequence into our formula. Here is the formula and the math:
tot = (last - first + 2) ÷ 2
tot = (172 - 38 + 2) ÷ 2
tot = 136 ÷ 2
tot = 68
Total even numbers from 37 to 173 = 68
Step 2) Calculate the sum of even numbers from 37 to 173
To calculate the sum of even numbers from 37 to 173, you enter the total even numbers (tot) from Step 1 and the first even number in the sequence into our formula. Here is the formula and the math:
sum = (tot ÷ 2) × (2 × first + (2 × (tot - 1))
sum = (68 ÷ 2) × (2 × 38 + (2 × (68 - 1))
sum = 34 × (76 + 134)
sum = 34 × 210
sum = 7140
Sum of even numbers from 37 to 173 = 7140
Step 3) Calculate the average of even numbers from 37 to 173
Almost done! Now we can calculate the average of even numbers from 37 to 173 by dividing the sum of even numbers from Step 2 by the total even numbers from Step 1. Here is the formula, the math, and the answer:
Average = sum ÷ tot
Average = 7140 ÷ 68
Average = 105
Average of even numbers from 37 to 173 = 105
Average of Even Numbers Calculator
Here you can calculate the average of even numbers of a different sequence.